Taylor coefficients of mock-Jacobi forms and moments of partition statistics

DOI10.1017/S0305004114000292zbMath1311.11039OpenAlexW2320226519MaRDI QIDQ2927883

Robert C. Rhoades, Kathrin Bringmann, Karl Mahlburg

Publication date: 4 November 2014

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004114000292

zbMATH Keywords

Taylor coefficientsHardy-Ramanujan circle methodmock-Jacobi forms

Mathematics Subject Classification ID

Applications of the Hardy-Littlewood method (11P55) Jacobi forms (11F50)

Related Items (21)

\({\mathrm {H}}\)-harmonic Maaß-Jacobi forms of degree 1 ⋮ The number of parts in certain residue classes of integer partitions ⋮ The first positive rank and crank moments for overpartitions ⋮ Higher order smallest parts functions and rank-Crank moment inequalities from Bailey pairs ⋮ Integer partitions, probabilities and quantum modular forms ⋮ Inequalities between first moments of \(M_2\)-rank and crank for overpartitions ⋮ On the number of parts of integer partitions lying in given residue classes ⋮ On the distribution of the \textsf{spt}-crank ⋮ Asymptotic formulas for spt-crank of partitions ⋮ Taylor coefficients of false Jacobi forms and ranks of unimodal sequences ⋮ Taylor expansions of Jacobi forms and linear relations among theta series ⋮ Inequalities for ranks of partitions and the first moment of ranks and cranks of partitions ⋮ The asymptotic distribution of the rank for unimodal sequences ⋮ Asymptotic inequalities for positive crank and rank moments ⋮ Asymptotic formulas related to the \(M_2\)-rank of partitions without repeated odd parts ⋮ Families of quasimodular forms and Jacobi forms: The crank statistic for partitions ⋮ Perspectives on mock modular forms ⋮ On the non-negativity of the spt-crank for partitions without repeated odd parts ⋮ Asymptotics of crank generating functions and Ramanujan congruences ⋮ On Dyson’s crank distribution conjecture and its generalizations ⋮ Asymptotic formulae for partition ranks

Cites Work

• Unnamed Item
• Higher order spt-functions
• On the explicit construction of higher deformations of partition statistics
• Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks
• Dyson's ranks and Maass forms
• Relations between the ranks and cranks of partitions
• On two geometric theta lifts
• Mappings and symmetries of partitions
• Zagier-type dualities and lifting maps for harmonic Maass-Jacobi forms
• Rank-crank type PDE's and non-holomorphic Jacobi forms
• On modular forms of half integral weight
• Asymptotic formulas for coefficients of Kac–Wakimoto Characters
• Rank-Crank type PDE's for higher level Appell functions
• CONGRUENCES FOR ANDREWS' SMALLEST PARTS PARTITION FUNCTION AND NEW CONGRUENCES FOR DYSON'S RANK
• Dyson’s crank of a partition
• On the asymptotic behavior of Kac-Wakimoto characters
• Asymptotics for rank and crank moments
• Inequalities between ranks and cranks
• Partition congruences and the Andrews-Garvan-Dyson crank
• Some Properties of Partitions

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